One solution could be to simply downgrade to the version indicated (in case this is possible). You can do this via (force version) in
synaptic graphically. Or you can be cool and use the command line:
sudo apt-get install libcairo2=1.10.2-6.1ubuntu2 --reinstall
sudo apt-get install libcairo-gobject2=1.10.2-6.1ubuntu2 --reinstall
In best case there will be no troubles on the way of "downgrading those two packages". I had the same problem and there was no problem.
The reason for the occurence of the problem in the first place is that
on your system the newer version have been installed. You have installed
libcairo2 (1.10.2-6.1ubuntu 3 ) and libcairo-gobject2 (1.10.2-6.1ubuntu 3 )
This can happend if one selects the "optional updates" (see picture)
in the source-packages-repositories-configureation. This will cause those new versions to be installed. This normaly is no problem at all. and no error message will occur.
But then if you later on deslect/unselect the "optional updates". Then the those packages (the new version) will still be kept installed, while the new installs (like your libcairo2-dev) will be requesting version that are older (because the repos/package-sources do not have those "optional updates" included anymore). Then there is the unmet dependency.
So theoreitcally it might also help to make sure that you have the "optional updates packages" selected.
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